By John Stuart Mill

ISBN-10: 0710075065

ISBN-13: 9780710075062

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Extra info for A System of Logic Ratiocinative and Inductive, Part II (The Collected Works of John Stuart Mill - Volume 08)

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In the next section, we identify useful, objective forms of knowledge that can be nicely encoded in ASP and we investigate how to represent them in FO(ID). 1 Representing Objective Knowledge in ASP and FO(ID) Representing UNA and DCA Implicitly, ASP maintains the Unique Names Assumption (UNA(Σ)) [27] that all ground terms of ΣF un represent different objects, and the Domain Closure Assumption (DCA(Σ)) [27] that each object in the universe is represented by at least one ground term of ΣF un . , databases), but neither UNA nor DCA are imposed in FO.

Theories. ), we are indebted to Michael Gelfond and Vladimir Lifschitz, whose work, as can be seen in this paper, has been a continous source of inspiration. References 1. : Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press, Cambridge (2003) 2. : Approximating general logic programs. In: ILPS, pp. 181–198 (1993) 3. : Expanding queries to incomplete databases by interpolating general logic programs. J. Log. Program. 35(3), 195–230 (1998) 4. : Competence in knowledge representation.

Let S be a set of arguments such that Cnl(S) is inconsistent. Let Y = N B(S) Hence Y is inconsistent. From the assumption-discrimination of CN, it follows that there is Z ⊆ Y such that A = (Z, α) is an argument. As N B(S) is a base of S, A is generated by S. Since A attacks each argument having α as an assumption, A attacks S. Hence S implicitly attacks itself. It follows immediately from lemma 3 and theorem 1 Theorem 2. Suppose CN is assumption-discriminate. Then the abstract assumption-based argumentation framework satisfies both the logical closure- and consistency-properties.

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A System of Logic Ratiocinative and Inductive, Part II (The Collected Works of John Stuart Mill - Volume 08) by John Stuart Mill

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